How would you distinguish one non-identical coin from a pile of nine coins where eight are identical?

Sure, here is a step-by-step guide to distinguish one non-identical coin from a pile of nine coins where eight are identical:

1. Divide the nine coins into three groups of three coins each.

2. Use a balance scale to weigh two of the three groups against each other. There are two possible outcomes:

   a. If the two groups weigh the same, the non-identical coin is in the third group that was not weighed.

   b. If the two groups do not weigh the same, the non-identical coin is in the group that weighs less or more (depending on whether the non-identical coin is lighter or heavier).

3. Now, you have a group of three coins, one of which is non-identical. Divide this group into three individual coins.

4. Weigh two of these coins against each other.

   a. If they weigh the same, the non-identical coin is the one that was not weighed.

   b. If they do not weigh the same, the non-identical coin is the one on the scale that weighs less or more.

By following these steps, you can identify the non-identical coin using the balance scale only twice.